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Abstract
Limit-cycle prediction of thermoacoustic instabilities for unstable practical gas turbine combustion systems is still a challenge for the gas turbine industry. The nonlinear stability analysis is especially demanding for highly turbulent swirling flames with significant equivalence ratio fluctuations. In the present study, a partially premixed swirl-stabilized flame at a Reynolds number of approximately 35,000 is investigated. An experimentally obtained flame describing function (FDF) is used for the determination of the thermoacoustic oscillation frequency and amplitude. Damping is obtained directly from measurements. The multi-microphone method is used to determine the amplitude dependent transfer function of the flame as well as the transfer function of the burner and the acoustic response of the boundary conditions. Solving the thermoacoustic modeling framework, with the measured transfer functions incorporated, yields frequency and amplitude of the self-excited limit cycle oscillation. The error between model and experimental results is thoroughly assessed. Measurements were made for various lengths of the combustion chamber exhaust gas tube to verify the results for different frequencies and amplitudes. Good agreement is found for the entire range of combustor lengths investigated. A sensitivity analysis of the linear flame transfer function to several operational parameters is provided allowing for an assessment of the limits of the nonlinear stability analysis approach. Furthermore, the effect of amplitude dependent damping is addressed.